The Logic and Metaphysics Workshop will meet on February 9th from 2:00-4:00 in-person at the Graduate Center (Room 9205) for a talk by Roman Kossak (CUNY).

Title: Petr Vopěnka’s new infinitary mathematics

Abstract: Petr Vopěnka (1935–2015) was an influential mathematician and deep and original thinker. In the 1970s, he developed  an axiomatic system of a non-Cantorial set theory, he called Alternative Set Theory (AST). I will present the  axioms of AST and the new concept of natural infinity on which they are based. I will also talk about how Vopěnka’s radical thoughts on the foundations of  mathematics evolved since the 1970s, as presented in his posthumously published book “New Infinitary Mathematics”.

The Logic and Metaphysics Workshop will meet on February 2nd from 2:00-4:00 in-person at the Graduate Center (Room 9205) for a talk by Xander MacSwan (CUNY).

Title: Why gaps and gluts don’t like De Morgans

Abstract: This paper explores the space of FDE sublogics which lack some combination of De Morgan Laws. A particular method is proposed for generating the sixteen logics, one for each combination of laws, by systematically applying what I will call modular alterations to standard FDE. Each alteration eliminates a particular De Morgan law from FDE both semantically, by making use of nondeterminism in the matrices, and proof theoretically, using rules that are derivable in FDE and are illustrative of contexts in which classical reasoning can be recaptured. The alterations are modular in that they are designed to be freely combinable, where each combination of alterations generates a unique member of the family of logics. After giving some independent philosophical motivation for the semantic and proof theoretic alterations, I will introduce each alteration in turn and prove soundness and completeness for the resulting logics. Finally, I will discuss the prospects of extending the same strategy to K3 and LP, for the definition of a material conditional, and of alternative methods for generating equivalent logics.

The Logic and Metaphysics Workshop will be meeting on Mondays from 2:00 to 4:00 pm at the CUNY Graduate Center (Room 9205) unless otherwise indicated. Talks will be in-person only. The provisional schedule is as follows:

Feb 2. Xander MacSwan (CUNY)

Feb 9. Roman Kossak (CUNY)

Feb 16. NO MEETING

Feb 23. Sara Ayhan (Tohoku)

Mar 2. James Walsh (NYU) [Room 9207]

Mar 9. Chris Steinsvold (CUNY) [Room TBA]

Mar 16. Liam Ryan (New York)

Mar 23. Jamie Beardmore (Columbia)

Mar 30. Shin Matsuura (CUNY)

Apr 6. NO MEETING

Apr 13. Eno Agolli (CUNY)

Apr 20. Jacopo Giraldo (Padua)

Apr 27. Mel Fitting (CUNY)

May 4. Marian Călborean (Bucharest)

May 11. Mircea Dumitru (Bucharest)

May 18. A farewell to Graham Priest (Special Event)